[en] A canonical transformation of an infinite set of differential equations describing the motion of the three-body system in the adiabatic basis is suggested. This transformation allows one to reduce the initial problem to the solution of a finite set of differential equations. As an example, a system of two bound differential equations is constructed. It represents the initial infinite set of equations with the accuracy of (2M)^-2, where M^-1 approximately msub(c)/Msub(o) is the ratio of the mass of the negative charged particle c to the reduced mass of two positive charged particles a and b. It is shown that the transformation suggested removes the difficulties in formulating the boundary conditions in adiabatic basis. The physical meaning of the transformation and solution obtained is discussed